How to find a cost function for human data
You've hit upon the central conundrum of supervised learning: if you want a machine to learn to do something, you need to know how to explain what that something is.

In the case of music, there are several possible approaches:


Make one set of "bad" songs, and one set of "good" songs. Develop a measure of how similar two songs are (maybe euclidian distance between their discrete Fourier transforms is a good starting place?). Your cost function is then based minimizing the average distance to "good" songs, and maximizing the average distance to "bad" songs. This may not work well though, because good and bad songs might differ only in the occasional misplaced notes.
Move to a reinforcement learning paradigm. Listen to each song proposed by your network. Give is a score based on your subjective enjoyment. Your cost function is based on maximizing this score. This might work well, but again, it might not. Music is tricky.
Use unsupervised approaches. Reward your network just for making something that resembles music (perhaps using the Fourier transform approach above), without labelling good and bad. The advantage is that you don't need to decide what is good or bad, and so you can use a lot more music in your dataset. The drawback is music as a whole might be too diverse to learn easily from examples.
Treat your music as a sequence of notes, and train a generative model to predict future notes on the basis of past notes. You can then generate new music by starting the model with a set of notes and letting it generate new ones for a long time.